> Interestingly computable numbers don't go to infinity: Computable numbers are an unbounded set, so in that sense they do go to infinity, just like the natura

> Interestingly computable numbers don't go to infinity: Computable numbers are an unbounded set, so in that sense they do go to infinity, just like the natural numbers go to infinity. They just aren't uncountable. Others and myself have noted in other comments that the Cantor notion of cardinality is not all that interesting or useful compared to the concepts of intuitionalism and constructivism. In particular, as noted in Wikipedia, "almost all real numbers are not computable", yet it is impossible (by definition) to actually produce or approximate one of these numbers through any sort of computational process. This sort of obvious nonsense is why mathematics has very very slowly been edging back from "Cantor's Paradise".